Hydromagnetic viscous flow in a rotating annular high-porosity medium with nonliner forchheimer drag effects: numerical study

A mathematical model is presented for the steady, axisymmetric, magnetohydrodynamic (MHD) flow of a viscous, Newtonian, incompressible, electrically-conducting liquid in a highly porous regime intercalated between two concentric rotating cylinders in the presence of a radial magnetic field. The porous medium is modeled using a Darcy-Forchheimer drag force approach to simulate the impedance effects of the porous medium fibers at both low velocities and also at higher velocities. The tangential and axial momentum equations are non-dimensionalized with the Nath transformations [33] and rendered into a system of nonlinear, second order, second degree partial differential conservation equations subject to appropriate nonslip boundary conditions. Solutions are obtained using both the MAPLE Library finite difference algorithm and the Network Simulation Method. The influence of Hartmann number (Ha), rotational Reynolds number (ReR), Darcy number (Da), Forchheimer number (Fs), pressure gradient parameter (α) and cylinder relative rotation rate (N) on the dimensionless tangential (Ue) and axial (UZ) velocity components is studied in detail for the case where the cylinder walls are insulated. Excellent agreement is achieved between both methods. Applications of this study include hybrid porous media MHD power generators, magnetic materials processing and chemical engineering.